nuisance parameters

(noun)

any parameter that is not of immediate interest but which must be accounted for in the analysis of those parameters which are of interest; the classic example of a nuisance parameter is the variance $\sigma^2$, of a normal distribution, when the mean, $\mu$, is of primary interest

Related Terms

Examples of nuisance parameters in the following topics:

  • When Does the Z-Test Apply?

    • Nuisance parameters should be known, or estimated with high accuracy (an example of a nuisance parameter would be the standard deviation in a one-sample location test).
    • $Z$-tests focus on a single parameter, and treat all other unknown parameters as being fixed at their true values.
    • In practice, due to Slutsky's theorem, "plugging in" consistent estimates of nuisance parameters can be justified.

  • Randomized Block Design

    • However, there are also several other nuisance factors.
    • Nuisance factors are those that may affect the measured result, but are not of primary interest.
    • All experiments have nuisance factors.
    • When we can control nuisance factors, an important technique known as blocking can be used to reduce or eliminate the contribution to experimental error contributed by nuisance factors.
    • Randomization is then used to reduce the contaminating effects of the remaining nuisance variables.

  • Randomized Design: Single-Factor

    • Completely randomized designs study the effects of one primary factor without the need to take other nuisance variables into account.
    • In the design of experiments, completely randomized designs are for studying the effects of one primary factor without the need to take into account other nuisance variables.
    • Discover how randomized experimental design allows researchers to study the effects of a single factor without taking into account other nuisance variables.

  • Corrosion

    • Corrosion is a common nuisance with real impact.

  • Interpreting confidence intervals

    • Incorrect language might try to describe the confidence interval as capturing the population parameter with a certain probability.
    • This is one of the most common errors: while it might be useful to think of it as a probability, the confidence level only quantifies how plausible it is that the parameter is in the interval.
    • Another especially important consideration of confidence intervals is that they only try to capture the population parameter.
    • Confidence intervals only attempt to capture population parameters.

  • Capturing the population parameter

    • A plausible range of values for the population parameter is called a confidence interval.
    • If we report a point estimate, we probably will not hit the exact population parameter.
    • On the other hand, if we report a range of plausible values – a confidence interval – we have a good shot at capturing the parameter.
    • If we want to be very certain we capture the population parameter, should we use a wider interval or a smaller interval?
    • Likewise, we use a wider confidence interval if we want to be more certain that we capture the parameter.

  • Three-Dimensional Coordinate Systems

    • A three dimensional space has three geometric parameters: $x$, $y$, and $z$.
    • Each parameter is perpendicular to the other two, and cannot lie in the same plane. shows a Cartesian coordinate system that uses the parameters $x$, $y$, and $z$.
    • Each parameter is labeled relative to its axis with a quantitative representation of its distance from its plane of reference, which is determined by the other two parameter axes.
    • The cylindrical system uses two linear parameters and one radial parameter:
    • Identify the number of parameters necessary to express a point in the three-dimensional coordinate system

  • Introduction to confidence intervals

    • A point estimate provides a single plausible value for a parameter.
    • Instead of supplying just a point estimate of a parameter, a next logical step would be to provide a plausible range of values for the parameter.
    • In this section and in Section 4.3, we will emphasize the special case where the point estimate is a sample mean and the parameter is the population mean.
    • In Section 4.5, we generalize these methods for a variety of point estimates and population parameters that we will encounter in Chapter 5 and beyond.
    • This video introduces confidence intervals for point estimates, which are intervals that describe a plausible range for a population parameter.

  • Parametric Equations

    • ., $x$ and $y$) are expressed in terms of a single third parameter.
    • is a parametric equation for the unit circle, where $t$ is the parameter.
    • The notion of parametric equation has been generalized to surfaces of higher dimension with a number of parameters equal to the dimension of the manifold (dimension one and one parameter for curves, dimension two and two parameters for surfaces, etc.)
    • For example, the simplest equation for a parabola $y=x^2$ can be parametrized by using a free parameter $t$, and setting $x=t$ and $y = t^2$.
    • This is a function of the derivatives of $x$ and $y$ with respect to the parameter $t$.

  • Level of Confidence

    • The proportion of confidence intervals that contain the true value of a parameter will match the confidence level.
    • Confidence intervals consist of a range of values (interval) that act as good estimates of the unknown population parameter .
    • However, in infrequent cases, none of these values may cover the value of the parameter.
    • This value is represented by a percentage, so when we say, "we are 99% confident that the true value of the parameter is in our confidence interval," we express that 99% of the observed confidence intervals will hold the true value of the parameter.
    • After a sample is taken, the population parameter is either in the interval made or not -- there is no chance.